Local and global error estimation in Nordsieck methods
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G. Yu. Kulikov
Abstract
This paper deals with asymptotically correct methods to evaluate the local and global errors of Nordsieck formulas applied to ordinary differential equations. It extends naturally the results developed by Kulikov and Shindin [Comp. Math. Math. Phys. (2000) 40, 1255–1275] in local and global error computation of multistep methods, but shows that Kulikov and Shindin's technique becomes more complicated when implemented in numerical methods, for which the concepts of consistency and quasi-consistency are not equivalent (see Skeel [SIAM J. Numer. Anal. (1976) 13, 664–685]). A new property termed super quasi-consistency is introduced and special cases of Nordsieck formulas with cheaper error estimation are found. Numerical examples are included to confirm practically the theory presented in this paper.
© de Gruyter 2008
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- Numerical models of the second and third orders for a momentumless turbulent wake dynamics in a linearly stratified medium
- Some approaches to local modelling of tsunami wave runup on a coast
- Local and global error estimation in Nordsieck methods
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Articles in the same Issue
- An algorithm for the solution of a tidal dynamics problem on a sphere
- Numerical models of the second and third orders for a momentumless turbulent wake dynamics in a linearly stratified medium
- Some approaches to local modelling of tsunami wave runup on a coast
- Local and global error estimation in Nordsieck methods
- A study of a parallel statistical modelling algorithm for solution of the nonlinear coagulation equation
- Two finite-difference schemes for calculation of Bingham fluid flows in a cavity
